Scanning X-Ray Diffraction Microscopy for Diamond Quantum Sensing

An understanding of nano- and microscale crystal strain in chemical-vapor-deposition diamond is crucial to the advancement of diamond quantum technologies. In particular, the presence of such strain and its characterization presents a challenge to diamond-based quantum sensing and information applications—as well as for future dark-matter detectors, where the directional information about incoming particles is encoded in crystal strain. Here, we exploit nanofocused scanning x-ray diffraction microscopy to quantitatively measure crystal deformation from defects in diamond with high spatial and strain resolution. The combination of information from multiple Bragg angles allows stereoscopic three-dimensional modeling of strain-feature geometry; the diffraction results are validated via comparison to optical measurements of the strain tensor based on spin-state-dependent spectroscopy of ensembles of nitrogen-vacancy centers in the diamond. Our results demonstrate both strain and spatial resolution sufficient for directional detection of dark matter via x-ray measurement of crystal strain and provide a promising tool for diamond growth analysis and improvement of defect-based sensing.

Figure 1

(a) An illustration of scanning x-ray diffraction microscopy (SXDM). A monochromatic beam of hard x rays (here, 11.2 keV) is focused to a 25-nm spot at the diamond sample surface. The x rays undergo Bragg diffraction and are collected by a pixelated detector. The beam is scanned across the sample surface and a diffraction pattern is collected at each position. The inset shows a simplified schematic of the beam profile (orange ring). The yellow bar illustrates a simple diffraction pattern, as would be imaged from a perfect bulk crystal. Crystal strain shifts the Bragg angle $\theta$, moving the diffraction pattern along the detector $2\theta$ axis. (b)–(d) Illustrations of different crystal-strain features discussed in this work. (b) Macroscopic strain gradients arise across the diamond; for example, due to cleavage of a diamond into segments. (c) Dislocation features incorporated during CVD-diamond sample growth may create regions of strained crystal. (d) Microscopic damage to the diamond crystal—such as nuclear recoils following a WIMP or neutrino impact—leave characteristic strain signatures associated with displaced carbon nuclei in the lattice.

Figure 2

Local strain features measured using SXDM on an HPHT diamond sample with a 22-nm scan step. Features are observed on length scales similar to the predicted strain from particle-induced crystal damage [18, 22] (see Sec. 5). These data are acquired via ($\overline{1}13$) diffraction; for details of the analysis method, see the text.

Figure 3

(a) A schematic for Hard X-ray Nanoprobe (HXN) interrogation of the (113) and ($\overline{1}13$) crystal planes on the CVD quantum sensing diamond. The green beam addresses the (113) plane, while the yellow beam addresses ($\overline{1}13$). Layers with different lattice spacings and orientations diffract x rays within the beam differently, creating the diffraction pattern of Fig. 4. Schematically represented diamond components: the high-purity CVD substrate (gray), the polishing-damage layer at the substrate surface (green), and the $\mathrm{N}$-$V$–doped CVD overgrowth layer (red), which contains strained growth-defect features (black). (b),(c) Schematics of a strained growth-defect feature as projected onto the surface by scans addressing the (b) (113) and (c) ($\overline{1}13$) crystal planes.

Figure 4

(a) The diffraction pattern in the CVD-diamond sample measured at a single x-ray beam position, which includes contributions from multiple layers of the diamond as sketched in Fig. 3. (b) The diffraction pattern of (a) after dividing by the local host-crystal diffraction profile (for details, see Sec. C of the Supplemental Material [24]). This ratio emphasizes the contribution from sharp small-length-scale strain features such as crystal growth defects or recoil-induced damage. Each column of pixels in (b) is summed, yielding a one-dimensional diffraction curve, four of which are shown in (c). Each diffraction curve is fitted to a Gaussian line shape to extract a centroid and line width. The centroid position gives the mean strain in the feature, while the line width depends on the thickness of the feature along the beam path. The line colors are chosen to approximately match the strain scale of Fig. 5.

Figure 5

A spatial map of the strain due to crystal dislocation features in one region of the CVD quantum sensing diamond, as measured with (113) diffraction. The gray color indicates x-ray beam positions that do not intersect a strain feature, as identified via a threshold on the amplitude of the background-subtracted diffraction curve [illustrated in Fig. 4]. The four most prominent features are labeled A–D to simplify discussion in the main text. The same region and features are also measured with ($\overline{1}13$) diffraction; for results, see Sec. G of the Supplemental Material [24]. The color-scale limits are chosen for legibility of internal strain within features, rather than enforced by the measurement. Note that the spatial resolution of this scan is set by the scanning step size of 200 nm, chosen to enable measurement of deep strain features over a relatively large field of view; the strain map shown here represents approximately 13 h of continuous data acquisition.

Figure 6

The three-dimensional geometric model of compressively strained volumes in the region shown in Fig. 5, determined from two x-ray projections and constrained by crystal-growth assumptions and an associated model of the strain features (see text). The volumes indicated have strain above a threshold of $2\times {10}^{-4}$. The labeled regions correspond with the labels in Fig. 5. For a schematic illustration of the projection of similar features to create data such as those presented in Fig. 5, see Sec. I of the Supplemental Material [24]. For further discussion of the creation of the three-dimensional model from projected stereoscopic data, see Sec. K of the Supplemental Material [24].

Figure 7

The sum of the strain-tensor elements measured using a quantum diamond microscope (QDM), overlain with a vertical projection of a three-dimensional geometric model of strain features derived from SXDM measurements. The color map and the corresponding scale bar represent strain measured with QDM, while the wire-frame objects are the projected model. The labeled features correspond with the labels in Figs. 5 and 6.

Figure 8

A comparison between the QDM strain-tensor measurements and the three-dimensional geometric model of growth-defect regions from SXDM measurements. The strain-tensor elements $ϵ(ij)$ give strain on the $i$ crystal plane in the $j$ direction; $ϵ$(Diag) is the normal strain, while the other tensor elements give shear strain. Constant offsets have been subtracted from QDM strain-tensor measurements to simplify comparison on common color scales.

Figure 9

The application of spatially resolved nanoscale strain measurement to dark-matter detection. (a) WIMP dark matter interacts with a carbon nucleus in a sectioned diamond target, triggering detector elements. (b) The triggered section is removed from target and imaged or scanned; crystal damage due to nuclear recoils is localized to a micrometer-cubed voxel. (c) Within the diamond section, the orientation and asymmetry of the damage track and the resulting nanoscale strain preserve information about the incident direction of the WIMP. This information can be read out using the scanning x-ray nanodiffraction techniques presented here. The pictured feature is crystal-lattice damage from a nuclear recoil track following a 10-keV impact between a WIMP and a carbon nucleus, simulated using the srim software [18, 40].

Figure 10

SXDM scans of representative “background” regions in the CVD quantum sensing diamond, away from large-scale strain features, demonstrate the absence of preexisting features that could be mistaken for WIMP recoil tracks. Each plot shows the number of detector counts arising from compressively strained diamond in the CVD overgrowth layer—for details, see Sec. C of the Supplemental Material [24]. (Note that in these plots we do not apply the background subtraction and strain analysis described in Sec. 2; instead, the total signal from any compressively strained diamond gives a better indication of the presence or absence of small or weak features.) (a) Despite an overall strain gradient, a 40-nm-increment scan of the nanoprobe does not find features with the approximately 100-nm length scale expected for WIMP tracks. (b) A scan of a different background region, this time with 20-nm increments, reveals extended dislocation bundles, which can be easily distinguished from WIMP recoil tracks by their length; again, no strain features are observed having $\le 100\mathrm{nm}$ scale in all three dimensions.